Dynamical variety of shapes in financial multifractality

The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves to evaluation of whether or not a time series is multifractal and width of the resulting singularity spectrum is considered a measure of the degree of complexity involved. However, the character of the complexity of time series generated by the natural processes usually appears much more intricate than such a bare statement can reflect. As an example, based on the long-term records of S&P500 and NASDAQ - the two world leading stock market indices - the present study shows that they indeed develop the multifractal features, but these features evolve through a variety of shapes, most often strongly asymmetric, whose changes typically are correlated with the historically most significant events experienced by the world economy. Relating at the same time the index multifractal singularity spectra to those of the component stocks that form this index reflects the varying degree of correlations involved among the stocks.Comment: 26 pages, 10 figure

Quantifying origin and character of long-range correlations in narrative texts

In natural language using short sentences is considered efficient for communication. However, a text composed exclusively of such sentences looks technical and reads boring. A text composed of long ones, on the other hand, demands significantly more effort for comprehension. Studying characteristics of the sentence length variability (SLV) in a large corpus of world-famous literary texts shows that an appealing and aesthetic optimum appears somewhere in between and involves selfsimilar, cascade-like alternation of various lengths sentences. A related quantitative observation is that the power spectra S(f) of thus characterized SLV universally develop a convincing `1/f^beta' scaling with the average exponent beta =~ 1/2, close to what has been identified before in musical compositions or in the brain waves. An overwhelming majority of the studied texts simply obeys such fractal attributes but especially spectacular in this respect are hypertext-like, "stream of consciousness" novels. In addition, they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals. Scaling of S(f) in the present context implies existence of the long-range correlations in texts and appearance of multifractality indicates that they carry even a nonlinear component. A distinct role of the full stops in inducing the long-range correlations in texts is evidenced by the fact that the above quantitative characteristics on the long-range correlations manifest themselves in variation of the full stops recurrence times along texts, thus in SLV, but to a much lesser degree in the recurrence times of the most frequent words. In this latter case the nonlinear correlations, thus multifractality, disappear even completely for all the texts considered. Treated as one extra word, the full stops at the same time appear to obey the Zipfian rank-frequency distribution, however.Comment: 28 pages, 8 figures, accepted for publication in Information Science

Exploitation of Memetics for Melodic Sequences Generation

Music, or in narrower sense, melodic contours of the aesthetically arranged pitches and the respective durations attracts our cognition since the beginning and now shaping the way we think in the complex life of culture. From evolutionary school of thoughts we could learn our perspective of seeing the musical diversity of folk songs in Indonesian archipelago by hypothesizing the aligning memes throughout the data sets. By regarding the memeplexes constructed from the the Zipf-Mandelbrot Law in melodic sequences and some mathematical characteristics of songs e.g.: gyration and spiraling effect, we construct evolutionary steps i.e.: genetic algorithm as tools for generating melodic sequences as an alternating computational methods to model the cognitive processes creating songs. While we build a melodic-contour generator, we present the enrichment on seeing the roles of limitless landscape of creativity and innovation guided by particular inspirations in the creation of work of art in general

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

On Multifractal Structure in Non-Representational Art

Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific color (``blobs''), as well as patterns formed by the luminance gradient between adjacent colors (``edges''). It is found that the analysis method applied to ``blobs'' cannot distinguish between artists of the same movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8. The method can distinguish between different types of images, however, as demonstrated by studying a radically different type of art. The data suggests that the ``edge'' method can distinguish between artists in the same movement, and is proposed to represent a toy model of visual discrimination. A ``fractal reconstruction'' analysis technique is also applied to the images, in order to determine whether or not a specific signature can be extracted which might serve as a type of fingerprint for the movement. However, these results are vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps

An Alternative Postulate to see Melody as “Language”

The paper proposes a way to see melodic features in music/songs in the terms of “letters” constituting “words”, while in return investigating the fulfillment of Zipf-Mandelbrot Law in them. Some interesting findings are reported including some possible conjectures for classification of melodic and musical artifacts considering several aspects of culture. The paper ends with some discussions related to further directions, be it enrichment in musicology and the possible plan for musical generative art